Specification and user’s guide corresponding author: Barry Smith

Immaterial entity

Rosse and Mejino provide the following rationale for including terms for surfaces, lines, and points in the FMA:

Although anatomical texts and medical terminologies with an anatomical content deal only superficially, if at all, with anatomical surfaces, lines, and points, it is nevertheless necessary to represent these entities explicitly and comprehensively in the FMA in order to describe boundary and adjacency relationships of material physical anatomical entities and spaces. [15]

note(immaterial entity)[Immaterial entities are divided into two subgroups:

1. 
   boundaries and sites, which bound, or are demarcated in relation, to material entities, and which can thus change location, shape and size and as their material hosts move or change shape or size (for example: your nasal passage; the hold of a ship; the boundary of Wales (which moves with the rotation of the Earth) [10, , ]);
   
2. 
   spatial regions, which exist independently of material entities, and which thus do not change.]
   

We define:

a(immaterial entity)[Definition: a is an immaterial entity = Def. a is an independent continuant that has no material entities as parts. [028-001]]

1. Continuant fiat boundary

a(continuant fiat boundary)[ Axiom: Every continuant fiat boundary is located at some spatial region at every time at which it exists] (but not necessarily at the same spatial region from one time to the next) [XXX-001].

Intuitively, note(continuant fiat boundary)[a continuant fiat boundary is a boundary of some material entity (for example: the plane separating the Northern and Southern hemispheres; the North Pole), or it is a boundary of some immaterial entity (for example of some portion of airspace).

Three basic kinds of continuant fiat boundary can be distinguished (together with various combination kinds []):

• 
  continuant fiat boundaries which delineate fiat parts within the interiors of material entities – for example the fiat boundary between the northern and southern hemispheres of the Earth; the North Pole; the fiat boundary which separates Utah from Colorado
  
• 
  continuant fiat boundaries which delineate holes or cavities, for example fiat boundaries of the type referred to by the FMA as ‘plane of anatomical orifice’.
  
• 
  combination continuant fiat boundaries such as the border of Israel, which contains both rectilinear fiat boundaries along the border with Egypt and fiat boundaries tracking physical discontinuities on the Mediterranean side and along the borders with Syria and Jordan.
  

zero-dimensional continuant fiat boundary

as(zero-dimensional continuant fiat boundary)[Examples: the geographic North Pole\; the quadripoint where the boundaries of Colorado, Utah, New Mexico, and Arizona meet\, the point of origin of some spatial coordinate system.]

one-dimensional continuant fiat boundary

as(one-dimensional continuant fiat boundary)[Examples: The Equator\, all geopolitical boundaries\, all lines of latitude and longitude\, the median sulcus of your tongue\, the line separating the outer surface of the mucosa of the lower lip from the outer surface of the skin of the chin. ]

To say that a one-dimensional continuant fiat boundary is continuous is to assert that it includes no gaps (thus it is a single straight or curved line).

two-dimensional continuant fiat boundary

‘Self-connected’ is to be understood in the usual topological sense: thus an entity b is self-connected if and only if: given any two points in b, a continuous line can be traced in b which connects these points.

From this it follows that a two-dimensional continuant fiat boundary (surface) may have holes, as for example in the case of the surface of one side of a compact disk.

2. Site

as(site)[Examples: a hole in the interior of a portion of cheese\, a rabbit hole\, the interior of your bedroom\, the Grand Canyon\, the Piazza San Marco\, an air traffic control region defined in the airspace above an airport\, the interior of a kangaroo pouch\, your left nostril (a fiat part – the opening – of your left nasal cavity) \, the lumen of your gut\, the hold of a ship\, the cockpit of an aircraft\, the interior of the trunk of your car\, the interior of your refrigerator\, the interior of your office\, Manhattan Canyon) ]

Each immaterial entity coincides at any given time with some spatial region, but, as in the case of material entities, which spatial region this is may vary with time. As the ship moves through space, so its hold moves also. As you pinch and unpinch your nose, so your nasal passages shrink and expand.

The above elucidations of site and of the different kinds of continuant fiat boundary will be replaced by definitions when dimension and boundary dependence have been defined within the BFO framework.

Note: Sites may be bounded by various combinations of boundaries of different sorts []. Thus the Mont Blanc Tunnel is bounded by fiat surfaces at either end.

Many of the terms used to refer to sites are ambiguous in that they are also used to refer to corresponding material entities. To say that ‘detergent is pumped into the tank_site’ is to assert that the detergent is pumped into the cavity which forms the interior of the tank_{material_entity} (rather than into, say, the portion of metal which bounds this cavity). To say that ‘Mary lives in Salzburg_site’ is to assert not that Mary lives in a certain material collection of buildings, ashphalt, rocks, trees, and so forth, but rather that she lives in the spatial niche [] bounded by this material collection.

Figure 5: Airspace classes

3. Spatial region

Given the terminology of spatial frames, we can elucidate ‘space’ as in BFO 1.1, as the maximal instance of the universal spatial region, relative to some frame, as follows:

a(spatial region)[Elucidation: A spatial region is a continuant entity that is a continuant_part_of space_R as defined relative to some frame R. [035-001]]

‘Maximal’, in the above, means that any instance entity including space_R as proper part is not a spatial region. Space_R is, in common parlance, the whole of space (as defined in reference to some frame R). The term ‘space’ is the name of a certain particular. As we shall see below, spacetime and time, similarly, are maximal instances of spatiotemporal and temporal region, respectively.

a(spatial region)[Axiom: All continuant parts of spatial regions are spatial regions. [036-001]]

Material entities have qualities of shape and size because they are located at spatial regions which instantiate corresponding shape and size universals.

Axiom: axiom(material entity)[Every material entity is located at some three-dimensional spatial region at every time at which it exists] [XXX-001]

Object boundaries and sites are distinguished from the spatial regions which they occupy at any given time as follows:

(1) Object boundaries and sites move when their material host moves, and they change shape or size when their material host changes shape or size.

(2) Spatial regions are, by definition, at rest relative to the pertinent coordinate frame.

zero-dimensional spatial region

one-dimensional spatial region

a(one-dimensional spatial region)[Examples: an edge of a cube-shaped portion of space.]

two-dimensional spatial region

as(two-dimensional spatial region)[Examples: the surface of a sphere-shaped part of space\, an infinitely thin plane in space. ]

three-dimensional spatial region (a spatial volume)

as(three-dimensional spatial region)[Examples: a cube-shaped region of space\, a sphere-shaped region of space,

]

4. Location